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Stephen G. Simpson - One of the best experts on this subject based on the ideXlab platform.
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Subsystems of Second Order Arithmetic, Second Edition, 2005. To be published by the Association For Symbolic Logic in their book series Perspectives in Logic. Chapter one of this book is available at: http://www.math.psu.edu/simpson/sosoa
2012Co-Authors: Stephen G. SimpsonAbstract:This talk represents joint work with Carl Mummert, my recent Ph.D. student at the Pennsylvania State University. Background: In my book SOSOA, a complete separable metric space is defined as the completion X = ( Â, ̂ d) of a countable pseudometric space (A, d). Here A ⊆ N and d: A × A → R. Thus complete separable metric spaces are “coded ” by countable objects. Using this coding, a great deal of analysis and geometry is developed in RCA0, with many reverse mathematics results. 3 A conceptual difficulty: Before Mummert/Simpson, there was no reverse mathematics study of general topology. The obstacle was, there was no way to discuss abstract topological spaces in L2, the language of second order arithmetic. This was the case even for topological spaces which are separable or second countable. The solution: We overcome this obstacle by introducing a restricted class of topological spaces, called countably based MF spaces. This class includes all complete separable metric spaces, as well as many nonmetrizable spaces. Furthermore, this class of spaces can be discussed in L2. 4 Let P be a poset, i.e., a partially ordered set. Definition. A Filter is a set F ⊆ P such that 1. F is upward closed, i.e., (q ≥ p ∧ p ∈ F) ⇒ q ∈ F. 2. for all p, q ∈ F there exists r ∈ F such that r ≤ p and r ≤ q. Compare the treatment of forcing in Kunen’s textbook of axiomatic set theory. Definition. A maximal Filter is a Filter which is not properly included in any other Filter. By Zorn’s Lemma, every Filter is included in a maximal Filter. Definition. MF(P) = {F | F is a maximal Filter on P}
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Subsystems of Second Order Arithmetic, Second Edition, Association for Symbolic Logic
Cambridge University Press, 2009Co-Authors: Stephen G. Simpson, In PressAbstract:2 Remark: This talk represents joint work with Carl Mummert, my recent Ph.D. student at the Pennsylvania State University. Background: In my book SOSOA, a complete separable metric space is defined as the completion X = ( Â, d) of a countable pseudometric space (A, d). Here A ⊆ N and d: A × A → R. Thus complete separable metric spaces are “coded ” by countable objects. Using this coding, a great deal of analysis and geometry is developed in RCA0, with many reverse mathematics results. 3 A conceptual difficulty: Before Mummert/Simpson, there was no reverse mathematics study of general topology. The obstacle was, there was no way to discuss abstract topological spaces in L2, the language of second order arithmetic. This was the case even for topological spaces which are separable or second countable. The solution: We overcome this obstacle by introducing a restricted class of topological spaces, called countably based MF spaces. This class includes all complete separable metric spaces, as well as many nonmetrizable spaces. Furthermore, this class of spaces can be discussed in L2. 4 Let P be a poset, i.e., a partially ordered set. Definition. A Filter is a set F ⊆ P such that 1. F is upward closed, i.e., (p ∈ F ∧ q ≥ p) ⇒ q ∈ F. 2. for all p, q ∈ F there exists r ∈ F such that p ≥ r ∧ q ≥ r. Compare the treatment of forcing in Kunen’s textbook of axiomatic set theory. Definition. A maximal Filter is a Filter which is not properly included in any other Filter. By Zorn’s Lemma, every Filter is included in a maximal Filter. Definition. MF(P) = {F | F is a maximal Filter on P}
Xin Zhang - One of the best experts on this subject based on the ideXlab platform.
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testing photometric redshift measurements with Filter Definition of the chinese space station optical survey css os
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Ye Cao, Yan Gong, Xianmin Meng, Xuelei Chen, Qi Guo, Dezi Liu, Y Q Xue, Li Cao, Xin ZhangAbstract:The Chinese Space Station Optical Survey (CSS-OS) is a major science project of the Space Application System of the China Manned Space Program. This survey is planned to perform both photometric imaging and slitless spectroscopic observations, and it will focus on different cosmological and astronomical goals. Most of these goals are tightly dependent on the accuracy of photometric redshift (photo-z) measurement, especially for the weak gravitational lensing survey as a main science driver. In this work, we assess if the current Filter Definition can provide accurate photo-z measurement to meet the science requirement. We use the COSMOS galaxy catalog to create a mock catalog for the CSS-OS. We compare different photo-z codes and fitting methods that using the spectral energy distribution (SED) template-fitting technique, and choose to use a modified LePhare code in photo-z fitting process. Then we investigate the CSS-OS photo-z accuracy in certain ranges of Filter parameters, such as band position, width, and slope. We find that the current CSS-OS Filter Definition can achieve reasonably good photo-z results with sigma_z~0.02 and outlier fraction ~3%.
Xuelei Chen - One of the best experts on this subject based on the ideXlab platform.
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testing photometric redshift measurements with Filter Definition of the chinese space station optical survey css os
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Ye Cao, Yan Gong, Xianmin Meng, Xuelei Chen, Qi Guo, Dezi Liu, Y Q Xue, Li Cao, Xin ZhangAbstract:The Chinese Space Station Optical Survey (CSS-OS) is a major science project of the Space Application System of the China Manned Space Program. This survey is planned to perform both photometric imaging and slitless spectroscopic observations, and it will focus on different cosmological and astronomical goals. Most of these goals are tightly dependent on the accuracy of photometric redshift (photo-z) measurement, especially for the weak gravitational lensing survey as a main science driver. In this work, we assess if the current Filter Definition can provide accurate photo-z measurement to meet the science requirement. We use the COSMOS galaxy catalog to create a mock catalog for the CSS-OS. We compare different photo-z codes and fitting methods that using the spectral energy distribution (SED) template-fitting technique, and choose to use a modified LePhare code in photo-z fitting process. Then we investigate the CSS-OS photo-z accuracy in certain ranges of Filter parameters, such as band position, width, and slope. We find that the current CSS-OS Filter Definition can achieve reasonably good photo-z results with sigma_z~0.02 and outlier fraction ~3%.
Ye Cao - One of the best experts on this subject based on the ideXlab platform.
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testing photometric redshift measurements with Filter Definition of the chinese space station optical survey css os
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Ye Cao, Yan Gong, Xianmin Meng, Xuelei Chen, Qi Guo, Dezi Liu, Y Q Xue, Li Cao, Xin ZhangAbstract:The Chinese Space Station Optical Survey (CSS-OS) is a major science project of the Space Application System of the China Manned Space Program. This survey is planned to perform both photometric imaging and slitless spectroscopic observations, and it will focus on different cosmological and astronomical goals. Most of these goals are tightly dependent on the accuracy of photometric redshift (photo-z) measurement, especially for the weak gravitational lensing survey as a main science driver. In this work, we assess if the current Filter Definition can provide accurate photo-z measurement to meet the science requirement. We use the COSMOS galaxy catalog to create a mock catalog for the CSS-OS. We compare different photo-z codes and fitting methods that using the spectral energy distribution (SED) template-fitting technique, and choose to use a modified LePhare code in photo-z fitting process. Then we investigate the CSS-OS photo-z accuracy in certain ranges of Filter parameters, such as band position, width, and slope. We find that the current CSS-OS Filter Definition can achieve reasonably good photo-z results with sigma_z~0.02 and outlier fraction ~3%.
Yan Gong - One of the best experts on this subject based on the ideXlab platform.
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testing photometric redshift measurements with Filter Definition of the chinese space station optical survey css os
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Ye Cao, Yan Gong, Xianmin Meng, Xuelei Chen, Qi Guo, Dezi Liu, Y Q Xue, Li Cao, Xin ZhangAbstract:The Chinese Space Station Optical Survey (CSS-OS) is a major science project of the Space Application System of the China Manned Space Program. This survey is planned to perform both photometric imaging and slitless spectroscopic observations, and it will focus on different cosmological and astronomical goals. Most of these goals are tightly dependent on the accuracy of photometric redshift (photo-z) measurement, especially for the weak gravitational lensing survey as a main science driver. In this work, we assess if the current Filter Definition can provide accurate photo-z measurement to meet the science requirement. We use the COSMOS galaxy catalog to create a mock catalog for the CSS-OS. We compare different photo-z codes and fitting methods that using the spectral energy distribution (SED) template-fitting technique, and choose to use a modified LePhare code in photo-z fitting process. Then we investigate the CSS-OS photo-z accuracy in certain ranges of Filter parameters, such as band position, width, and slope. We find that the current CSS-OS Filter Definition can achieve reasonably good photo-z results with sigma_z~0.02 and outlier fraction ~3%.