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Some Aspects and Examples of Infinity NotionsMathematical Logic Quarterly 40 (1): 111-124. 2006.Our main contribution is a formal definition of what could be called a T‐notion of infinity, for set theories T extending ZF. Around this definition we organize some old and new notions of infinity; we also indicate some easy independence proofs. Mathematics Subject Classification: 03E25, 03E20.
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There Can Be a Permutation Which Is Not The Product of Two ReflectionsMathematical Logic Quarterly 34 (1): 65-66. 2006.
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57There Can Be a Permutation Which Is Not The Product of Two ReflectionsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (1): 65-66. 1988.
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43There Can Be a Permutation Which Is Not The Product of Two ReflectionsMathematical Logic Quarterly 34 (1): 65-66. 1988.
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73Some Aspects and Examples of Infinity NotionsMathematical Logic Quarterly 40 (1): 111-124. 1994.I wish to thank Klaus Kühnle who streamlined in [8] several of my definitions and proofs concerning the subject matter of this paper. Some ideas and results arose from discussions with Klaus Leeb. Jan Johannsen discovered some mistakes in an earlier version.
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129Das onto-logische SechseckGrazer Philosophische Studien 32 (1): 113-121. 1988.Das onto-logische Sechseck ist eine Erweiterung des (aristotelischen) onto-logischen Vierecks um singuläre und universelle Sachverhalte. Beide Vielecke inkorporieren ontische, logische und ontisch-logische Relationen. Dies ist der Grund für die Bindestrichschreibung "ontologisch". Das onto-logische Sechseck liefert die Grundlage für eine neue Definition der Wahrheit eines Satzes.
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121Towards intuitionistic dynamic logicLogic and Logical Philosophy 15 (4): 305-324. 2006.We propose the beginnings of an intuitionistic propopsitional dynamic logic, and describe several serious open problems.
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154Complete infinitary type logicsStudia Logica 63 (1): 85-119. 1999.For each regular cardinal κ, we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are $\Sigma _{}$, the global system $\text{g}\Sigma _{}$ and the τ-system $\tau \Sigma _{}$. A full cut elimination theorem is proved for the local systems, and about the τ-systems we prove that they admit cut-free proofs for sequents in the τ-free language common to the local and global systems. These two results follow from semantic …Read more
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Proof Theory For Finitely Valid SentencesReports on Mathematical Logic 47-59. 2001.We investigate infinitary sequent calculi which generate the finitely valid sentences of first-order logic, of simple type theory and of transitive closure logic, respectively.
