Topics in Logic and Foundations: Spring 2004
نویسنده
چکیده
This is a set of lecture notes from a 15-week graduate course at the Penn-sylvania State University taught as Math 574 by Stephen G. Simpson in Spring 2004. The course was intended for students already familiar with the basics of mathematical logic. The course covered some topics which are important in contemporary mathematical logic and foundations but usually omitted from introductory courses at Penn State. These notes were typeset by the students in the course: Todt. In addition, the notes were revised and polished by Stephen Simpson.
منابع مشابه
Ultraproducts, the Compactness Theorem and Applications
This is a set of lecture notes used in a course on model theory at Virginia Commonwealth University (Math 591 Topics: Logic and Mathematical Structures), which I taught jointly with Sean Cox in the spring of 2014. Most of the material contained in these notes can be found in the following sources. References: • Chang and Keisler. Model Theory, Studies in Logic and the Foundations of Mathematics...
متن کاملDo Not Claim Too Much: Second-order Logic and First-order Logic
The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Second-
متن کاملPlausible and Paradoxical Reasoning
Foundations for a new theory of plausible and paradoxical reasoning Abstract Albena Tchamova and Tzvetan Semerdjiev Fuzzy Logic Approach to Estimating Tendencies in Target Behavior Abstract Tzvetan Semerdjiev Abstract Ljudmil V. Bojilov
متن کاملMathematical Fuzzy Logic: An Invitation to Interesting Research Areas
The paper discusses some core topics which present open problems in the field of mathematical fuzzy logic and in the foundations of fuzzy set theory. It may reasonably be assumed that these problems shall have great influence for the future development of fuzzy logic within the next decade.
متن کاملPOWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...
متن کامل