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Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
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References
- ↑ Corazza, Paul (2000), "The Wholeness Axiom and Laver Sequences", Annals of Pure and Applied Logic, 105 (1–3): 157–260, doi: 10.1016/s0168-0072(99)00052-4
- ↑ Samuel Gomes da Silva, Review of "The wholeness axioms and the class of supercompact cardinals" by Arthur Apter.
- ↑ Holmes, M. Randall; Forster, Thomas; Libert, Thierry (2012), "Alternative set theories", Sets and extensions in the twentieth century, Handb. Hist. Log., vol. 6, Elsevier/North-Holland, Amsterdam, pp. 559–632, doi:10.1016/B978-0-444-51621-3.50008-6, MR 3409865 .
- 1 2 Hamkins, Joel David (2001), "The wholeness axioms and V = HOD", Archive for Mathematical Logic, 40 (1): 1–8, arXiv: math/9902079 , doi:10.1007/s001530050169, MR 1816602, S2CID 15083392 .
- ↑ Apter, Arthur W. (2012), "The wholeness axioms and the class of supercompact cardinals", Bulletin of the Polish Academy of Sciences, Mathematics, 60 (2): 101–111, doi:10.4064/ba60-2-1, MR 2914539 .