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H. Luckhardt [6]Horst Luckhardt [3]
  1. Horst Luckhardt (1996). Bounds Extracted by Kreisel From Ineffective Proofs. In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel. A K Peters. 289--300.
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  2. H. Luckhardt (1991). Complexity Versus the Church‐Rosser Property and Confluence. Mathematical Logic Quarterly 37 (5‐6):85-92.
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  3. H. Luckhardt (1989). Herbrand Analysis of 2 Proofs of the Roth Theorem-Polynomial Bounds. Journal of Symbolic Logic 54 (1):234-263.
     
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  4. H. Luckhardt (1989). Herbrand-Analysen Zweier Beweise Des Satzes Von Roth: Polynomiale Anzahlschranken. Journal of Symbolic Logic 54 (1):234-263.
    A previously unexplored method, combining logical and mathematical elements, is shown to yield substantial numerical improvements in the area of Diophantine approximations. Kreisel illustrated the method abstractly by noting that effective bounds on the number of elements are ensured if Herbrand terms from ineffective proofs of Σ 2 -finiteness theorems satisfy certain simple growth conditions. Here several efficient growth conditions for the same purpose are presented that are actually satisfied in practice, in particular, by the proofs of Roth's theorem due (...)
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  5. W. Friedrich & H. Luckhardt (1980). Intuitionistic Uniformity Principles for Propositions and Some Applications. Studia Logica 39 (4):361 - 369.
    This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no (...)
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  6. H. Luckhardt (1980). On Constructive Functions Ranging Over Propositions. Studia Logica 39 (4):371 - 374.
    It is shown that there is no constructive extensional truth-value mapping from the speciesP of all propositions into known constructive structures P.
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  7. H. Luckhardt (1979). A Limit for Higher Recursion Theory. Mathematical Logic Quarterly 25 (30):475-479.
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  8. Horst Luckhardt (1975). A Short Proof of a Well‐Known Theorem of Intuitionistic Analysis. Mathematical Logic Quarterly 21 (1):185-186.
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  9. Horst Luckhardt (1973). Extensional Gödel Functional Interpretation. New York,Springer-Verlag.
     
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