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Mihai Ganea
University of Toronto, St. George Campus
  1.  35
    Burgess' PV Is Robinson's Q.Mihai Ganea - 2007 - Journal of Symbolic Logic 72 (2):619 - 624.
    In [2] John Burgess describes predicative versions of Frege's logic and poses the problem of finding their exact arithmetical strength. I prove here that PV, the simplest such theory, is equivalent to Robinson's arithmetical theory Q.
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  2.  37
    Arithmetic on Semigroups.Mihai Ganea - 2009 - Journal of Symbolic Logic 74 (1):265-278.
    Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be mutually interpretable with TC, a weak theory of concatenation introduced by Grzegorczyk. Furthermore, TC is shown to be interpretable in the theory F studied by Tarski and Szmielewa, thus confirming their claim that F is essentially undecidable.
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  3. Two (or Three) Notions of Finitism.Mihai Ganea - 2010 - Review of Symbolic Logic 3 (1):119-144.
    Finitism is given an interpretation based on two ideas about strings (sequences of symbols): a replacement principle extracted from Hilberts class 2 can be justified by means of an additional finitistic choice principle, thus obtaining a second equational theory . It is unknown whether is strictly stronger than since 2 may coincide with the class of lower elementary functions.
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  4.  75
    Epistemic Optimism.Mihai Ganea - 2008 - Philosophia Mathematica 16 (3):333-353.
    Michael Dummett's argument for intuitionism can be criticized for the implicit reliance on the existence of what might be called absolutely undecidable statements. Neil Tennant attacks epistemic optimism, the view that there are no such statements. I expose what seem serious flaws in his attack, and I suggest a way of defending the use of classical logic in arithmetic that circumvents the issue of optimism. I would like to thank an anonymous referee for helpful comments. CiteULike Connotea Del.icio.us What's this?
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  5.  21
    Finitistic Arithmetic and Classical Logic.Mihai Ganea - 2014 - Philosophia Mathematica 22 (2):167-197.
    It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational reasoning to classical quantifier logic in arithmetic. The conclusion reached is that Edward Nelson's ‘predicative arithmetic’ program, which makes essential use of classical quantifier logic, cannot be justified finitistically and thus requires a different philosophical foundation, possibly (...)
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  6. On the Grammar of First-Order Logic.Mihai Ganea - 2013 - Romanian Journal of Analytic Philosophy 7 (1):5 - 18.
  7. A Remark on a Relational Version of Robinson’s Arithmetic Q.Mihai Ganea - 2015 - In Iulian D. Toader, Gabriel Sandu & Ilie Pȃrvu (eds.), Romanian Studies in Philosophy of Science. Springer Verlag.
     
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