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  1. Pavel Hrubeš (2009). Kreisel's Conjecture with Minimality Principle. Journal of Symbolic Logic 74 (3):976-988.
    We prove that Kreisel's Conjecture is true, if Peano arithmetic is axiomatised using minimality principle and axioms of identity (theory $PA_M $ )-The result is independent on the choice of language of $PA_M $ . We also show that if infinitely many instances of A(x) are provable in a bounded number of steps in $PA_M $ then there existe k ∈ ω s. t. $PA_M $ ┤ ∀x > k̄ A(x). The results imply that $PA_M $ does not prove scheme (...)
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  2. Pavel Hrubeš (2009). On Lengths of Proofs in Non-Classical Logics. Annals of Pure and Applied Logic 157 (2):194-205.
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  3. Gregory L. Cherlin, Ilijas Farah, Pavel Hrubes, Victor Marek, Jan Riemann, Simon Thomas & Jeffrey Remmel (2008). San Diego Convention Center, San Diego, CA January 8–9, 2008. Bulletin of Symbolic Logic 14 (3).
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  4. Pavel Hrubeš (2007). A Lower Bound for Intuitionistic Logic. Annals of Pure and Applied Logic 146 (1):72-90.
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  5. Pavel Hrubeš (2007). Lower Bounds for Modal Logics. Journal of Symbolic Logic 72 (3):941 - 958.
    We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ₁, ψ₂,... s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel—Löb's logic, S and S4. We also determine some speed-up relations between different systems of modal logic on formulas of modal-depth one.
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  6. Pavel Hrubeš (2007). Theories Very Close to PA Where Kreisel's Conjecture Is False. Journal of Symbolic Logic 72 (1):123 - 137.
    We give four examples of theories in which Kreisel's Conjecture is false: (1) the theory PA(-) obtained by adding a function symbol minus, '−', to the language of PA, and the axiom ∀x∀y∀z (x − y = z) ≡ (x = y + z ⋁ (x < y ⋀ z = 0)); (2) the theory T of integers; (3) the theory PA(q) obtained by adding a function symbol q (of arity ≥ 1) to PA, assuming nothing about q; (4) the (...)
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