7 found
  1.  39
    Reverse Mathematics and Well-Ordering Principles: A Pilot Study.Bahareh Afshari & Michael Rathjen - 2009 - Annals of Pure and Applied Logic 160 (3):231-237.
    The larger project broached here is to look at the generally sentence “if X is well-ordered then f is well-ordered”, where f is a standard proof-theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded ω-models for a particular theory Tf whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function f. To illustrate this theme, (...)
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  2.  12
    Herbrand's Theorem as Higher Order Recursion.Bahareh Afshari, Stefan Hetzl & Graham E. Leigh - 2020 - Annals of Pure and Applied Logic 171 (6):102792.
  3.  23
    A Note on the Theory of Positive Induction, $${{\rm ID}^*_1}$$.Bahareh Afshari & Michael Rathjen - 2010 - Archive for Mathematical Logic 49 (2):275-281.
    The article shows a simple way of calibrating the strength of the theory of positive induction, ${{\rm ID}^{*}_{1}}$ . Crucially the proof exploits the equivalence of ${\Sigma^{1}_{1}}$ dependent choice and ω-model reflection for ${\Pi^{1}_{2}}$ formulae over ACA 0. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of ${{\rm ID}^{*}_{1}}$ in Probst, J Symb Log, 71, 721–746, 2006.
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    Cyclic Proofs for the First-Order Μ-Calculus.Bahareh Afshari, Sebastian Enqvist & Graham E. Leigh - forthcoming - Logic Journal of the IGPL.
    We introduce a path-based cyclic proof system for first-order $\mu $-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal $\mu $-calculus.
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    Individual Members 2006.Martın Abadi, Yoshihiro Abe, Francine F. Abeles, Andrew Aberdein, Nathanael Ackerman, Bryant Adams, Klaus T. Aehlig, Fritz Aeschbach, Henry Louis Africk & Bahareh Afshari - 2006 - Bulletin of Symbolic Logic 12 (4):625-681.
  6.  24
    Ordinal Analysis and the Infinite Ramsey Theorem.Bahareh Afshari & Michael Rathjen - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 1--10.
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    Herbrand Confluence for First-Order Proofs with Π2-Cuts.Graham E. Leigh, Stefan Hetzl & Bahareh Afshari - 2016 - In Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science. De Gruyter. pp. 5-40.
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