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Two proof-theoretic remarks on EA + ECT

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Halbach_2-1o9cnbabmvlb83.pdf
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2000

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Halbach, Volker

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Mathematical Logic Quarterly. Wiley. 2000, 46(4), pp. 461-466. ISSN 0942-5616. eISSN 1521-3870. Available under: doi: 10.1002/1521-3870(200010)46:4<461::AID-MALQ461>3.0.CO;2-I

Zusammenfassung

In this note two propositions about the epistemic formalization of Church's Thesis (ECT) are proved. First it is shown that all arithmetical sentences deducible in Shapiro's system EA of Epistemic Arithmetic from ECT are derivable from Peano Arithmetic PA + uniform reflection for PA. Second it is shown that the system EA + ECT has the epistemic disjunction property and the epistemic numerical existence property for arithmetical formulas.

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100 Philosophie

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Epistemic Arithmetic, Church’s Thesis, Epistemic Logic

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ISO 690HALBACH, Volker, Leon HORSTEN, 2000. Two proof-theoretic remarks on EA + ECT. In: Mathematical Logic Quarterly. Wiley. 2000, 46(4), pp. 461-466. ISSN 0942-5616. eISSN 1521-3870. Available under: doi: 10.1002/1521-3870(200010)46:4<461::AID-MALQ461>3.0.CO;2-I
BibTex
@article{Halbach2000proof-56945,
  year={2000},
  doi={10.1002/1521-3870(200010)46:4<461::AID-MALQ461>3.0.CO;2-I},
  title={Two proof-theoretic remarks on EA + ECT},
  number={4},
  volume={46},
  issn={0942-5616},
  journal={Mathematical Logic Quarterly},
  pages={461--466},
  author={Halbach, Volker and Horsten, Leon}
}
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