Tanaka's theorem revisited

DOI10.1007/S00153-020-00720-ZzbMath1461.03055arXiv1811.08514OpenAlexW3100890379MaRDI QIDQ2204369

Saeideh Bahrami

Publication date: 15 October 2020

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08514

zbMATH Keywords

fixed pointPeano arithmeticself-embeddingnonstandard modelstrong cut\(\text{WKL}_0\)

Mathematics Subject Classification ID

Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62) Second- and higher-order arithmetic and fragments (03F35) Model theory of denumerable and separable structures (03C15)

Cites Work

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• Nonstandard second-order arithmetic and Riemann's mapping theorem
• The self-embedding theorem of \(\text{WKL}_ 0\) and a non-standard method
• The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic
• Fixed points of self-embeddings of models of arithmetic
• Unifying the model theory of first-order and second-order arithmetic via \(\mathrm{WKL}_0^\ast\)
• Models and types of Peano's arithmetic
• A non-standard construction of Haar measure and weak König's lemma

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