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Two Proof‐Theoretic Remarks on EA + ECT
Author(s) -
Halbach Volker,
Horsten Leon
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200010)46:4<461::aid-malq461>3.0.co;2-i
Subject(s) - peano axioms , arithmetic function , mathematics , property (philosophy) , reflection (computer programming) , arithmetic , second order arithmetic , calculus (dental) , algebra over a field , pure mathematics , discrete mathematics , epistemology , philosophy , computer science , medicine , dentistry , programming language
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.