## Logic Colloquium ’98

Proceedings of the Annual European Summer

Meeting of the Association for Symbolic Logic,

held in Prague, Czech Republic

August 9-15, 1998

Sam Buss, Petr Hajek, Pavel Pudlak, editors

Year: 2000

ISBN:1-56881-113-6

560 pages. Hardcover.

Year: 2000

ISBN: 1-56881-114-4

560 pages. Paperback.

This book is the proceedings of the 1998 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium ’98. The meeting was held at the University of Economics in Prague, August 9-15, 1998. This volume contains papers covering current research from all areas of mathematical logic, including Proof Theory, Set Theory, Model Theory, Computability Theory, and Philosophy. There are twelve articles on Proof Theory; a survey of fuzzy logic; nine articles on Set Theory; four articles on H. Rogers’ 1965 agenda for recursive function theory; four articles on Model Theory; and two articles on Belief Theories. A number of these articles deal with theoretical computer science.

### Table of Contents

- Opening speech.

Petr Vopenka - Bolzano Medal acceptance speech.

Gaisi Takeuti - Collapsing polynomial-time degrees.

K. Ambos-Spies, L. Bentzien, P. A. Fejer, W. Merkle, and F. Stephan. - Qualitative and probabilistic models of full belief.

H. Arl Costa - Relative splittings of $0^\prime_e$ in the $\Delta^0_2$-enumeration degrees.

M. M. Arslanov and A. Sorbi - A realizability interpretation for classical arithmetic.

J. Avigad - An axiomatization of quantified propositional Godel logic using the Takeuti-Titani rule.

M. Baaz and H. Veith - Another pathological well-ordering.

L. Beklemishev - How small can the set of generics be?

J. Brendle - Entailment relations and distributive lattices.

J. Cederquist and T. Coquand - The Friedberg jump inversion theorem revisited: a study of undefinable cuts.

C. T. Chong, L. Qian, and Y. Yang - Hartley Rogers’ 1965 agenda.

S. B. Cooper - Liftings of homomorphisms between quotient structures and Ulam stability.

I. Farah - Mathematical fuzzy logic – state of art.

P. Hajek - Reflections on the last Delfino problem.

K. Hauser - Continuous images of coanalytic sets.

G. Hjorth - Classification of subsheaves over GL-algebras.

U. H$FBhle - On the $\Delta^b_1$ bit-comprehension rule.

J. Johannsen and C. Pollett - Cardinal invariants associated with predictors.

S. Kamo - A theorem on countable ordered sets with an application to universal graphs.

P. Komjath - Dimension theory and smooth stratification of rigid subanalytic sets.

L. Lipshitz and Z. Robinson - The Ramsey structure of A-determined sets in a $\kappa$-saturated universe.

J. Mlcek and P. Zlatos - On $\Sigma$-Definability of admissible sets.

A. S. Morozov - Additive theories.

E. A. Palyutin - Adding multiplication to an o-minimal expansion of the additive group of real numbers.

Y. Peterzil, P. Speissegger, and S. Starchenko - The superjump in Martin-Lof type theory.

M. Rathjen - “Just because”: Taking belief bases seriously.

H. Rott - Artin approximation via the model theory of Cohen-Macaulay rings.

H. Schoutens - Ordinal systems, part 2: one inaccessible.

A. Setzer - Autonomous fixed point progressions and fixed point transfinite recursion.

T. Strahm - Finitary reductions for local predicativity, I: recursively regular ordinals.

S. Tupailo - The complexity of linear logic with weakening.

A. Urquhart - Some remarks on the maximality of inner models.

P. D. Welch