Reverse mathematics of first-order theories with finitely many models
- Author
- David Bélanger (UGent)
- Organization
- Abstract
- We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA(0), WKL0, or ACA(0). We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA(0) over RCA(0).
- Keywords
- number of models, reverse mathematics, effective model theory
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8669023
- MLA
- Bélanger, David. “Reverse Mathematics of First-Order Theories with Finitely Many Models.” JOURNAL OF SYMBOLIC LOGIC, vol. 79, no. 3, 2014, pp. 955–84, doi:10.1017/jsl.2014.32.
- APA
- Bélanger, D. (2014). Reverse mathematics of first-order theories with finitely many models. JOURNAL OF SYMBOLIC LOGIC, 79(3), 955–984. https://doi.org/10.1017/jsl.2014.32
- Chicago author-date
- Bélanger, David. 2014. “Reverse Mathematics of First-Order Theories with Finitely Many Models.” JOURNAL OF SYMBOLIC LOGIC 79 (3): 955–84. https://doi.org/10.1017/jsl.2014.32.
- Chicago author-date (all authors)
- Bélanger, David. 2014. “Reverse Mathematics of First-Order Theories with Finitely Many Models.” JOURNAL OF SYMBOLIC LOGIC 79 (3): 955–984. doi:10.1017/jsl.2014.32.
- Vancouver
- 1.Bélanger D. Reverse mathematics of first-order theories with finitely many models. JOURNAL OF SYMBOLIC LOGIC. 2014;79(3):955–84.
- IEEE
- [1]D. Bélanger, “Reverse mathematics of first-order theories with finitely many models,” JOURNAL OF SYMBOLIC LOGIC, vol. 79, no. 3, pp. 955–984, 2014.
@article{8669023, abstract = {{We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA(0), WKL0, or ACA(0). We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA(0) over RCA(0).}}, author = {{Bélanger, David}}, issn = {{0022-4812}}, journal = {{JOURNAL OF SYMBOLIC LOGIC}}, keywords = {{number of models,reverse mathematics,effective model theory}}, language = {{eng}}, number = {{3}}, pages = {{955--984}}, title = {{Reverse mathematics of first-order theories with finitely many models}}, url = {{http://doi.org/10.1017/jsl.2014.32}}, volume = {{79}}, year = {{2014}}, }
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