Logic and Foundations of Mathematics

1. Front Matter

   Pages i-viii

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2. Operations, Collections and Sets within a General Axiomatic Framework

   • Marco Forti, Furio Honsell, Marina Lenisa

   Pages 1-24

3. Some Ins and Outs of Indispensability: A Modal-Structural Perspective

   • Geoffrey Hellman

   Pages 25-39

4. Carnap’s Remarks on Impredicative Definitions and the Genericity Theorem

   • Thomas Fruchart, Giuseppe Longo

   Pages 41-55

5. Gödel, Turing, and K-Graph Machines

   • Wilfried Sieg, John Byrnes

   Pages 57-66

6. Linear Recurrence Relations are Δ0 Definable

   • Alessandro Berarducci, Benedetto Intrigila

   Pages 67-81

7. On Applicative Theories

   • Gerhard Jäger, Reinhard Kahle, Thomas Strahm

   Pages 83-92

8. The Use of a Logical Principle of Uniform Boundedness in Analysis

   • Ulrich Kohlenbach

   Pages 93-106

9. Epsilon-Substitution Method for the Ramified Language and \(\Delta _1^1\)-Comprehension Rule

   • Grigori Mints, Sergei Tupailo

   Pages 107-130

10. The Abstract Compactness Theorem Revisited

    • Xavier Caicedo

    Pages 131-141

11. On Sets Enclosed Between a Set and Its Double Complement

    • Wim Veldman

    Pages 143-154

12. Binary Relations in the Social and Mathematical Sciences

    • J. Lambek

    Pages 155-163

13. Basic Logic and the Cube of its Extensions

    • Giulia Battilotti, Giovanni Sambin

    Pages 165-186

14. Some Observations on Noncommutative Substructural Logics

    • Hiroakira Ono

    Pages 187-194

15. On Predicate Logic as Modal Logic

    • Dag Westerståhl

    Pages 195-207

16. A First-Order Effect and Modal Propositional Formulas

    • A. V. Chagrov

    Pages 209-217

17. Herbrand’s Theorem for a Modal Logic

    • Melvin Fitting

    Pages 219-225

18. Intuitionistic Modal Logic

    • Frank Wolter, Michael Zakharyaschev

    Pages 227-238

19. Dynamic Datastructures

    • Herman R. Jervell

    Pages 239-247

20. Resolution and the Decision Problem

    • Alexander Leitsch

    Pages 249-269

The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS­ studies.

• Philosophy of Science
• Rudolf Carnap
• compactness theorem
• logic
• modal logic
• model theory
• predicate logic
• proof theory
• proposition
• science
• set theory

• University of Florence, Italy

  Andrea Cantini, Pierluigi Minari

• Scuola Normale Superiore, Pisa, Italy

  Ettore Casari

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