Advanced Topics in Mathematical Logic - Descriptive Set Theory (V5A7) Geschke, Schlicht Bachelor-, Master-, Diplom-, and Ph.D. seminar Geschke, Koepke Graduate Seminar on Logic - … For example, a deck of cards, every student enrolled in Math 103, the collection of all even integers, these are all examples of sets of things. Projects for a master thesis can be chosen from all research areas of the Logic Group as well as from other fields of mathematical logic. This allows for a pleasing elegance: it seems we can understand and construct many phenomena from very intuitive and basic assumptions. Ordinals and cardinals Well-orderings and order-types. These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. 17.5 Set theory. 1. The set theory course is accompanied by advanced courses on other topics in mathematical logic and by graduate seminars in logic and set theory. 9.6 Alephs. PART III Related Topics Chapter 10 LOGIC AND PROPOSITIONAL CALCULUS • 229 1,0.1 Introduction. [5] Posets and Zorn’s lemma Partially ordered sets; Hasse diagrams, chains, maximal elements. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. Induction and recursion for ordinals. Cardinal and Ordinal Numbers. 3. The need for a rigorous treatment of the infinite in mathematics LOGIC AND SET THEORY (D) No specific prerequisites. 2. Learn about the logical foundations of such mathematical concepts as number, continuity and set. Set Theory and Logic Supplementary Materials Math 103: Contemporary Mathematics with Applications A. Calini, E. Jurisich, S. Shields c 2008. Ordinal arithmetic. We will need only a few facts about sets and techniques for dealing with them, which we set out in this section and the next. Understand the concept of infinity and its role in mathematics. 10.2 Propositions and Compound Propositions. Cardinals; the hierarchy of alephs. Using very simple principles, set theory allows us to construct some of the most complex elements of logic and mathematics. 10.5 Tautologies and Contradictions. Like logic, the subject of sets is rich and interesting for its own sake. 10.7 Algebra of Propositions. Select topic Subtopics: Algebra and number theory ... Logic and set theory; Mathematics - general; Probability, statistics, combinatorial theory; Topology; Trigonometry; Subtopic: Logic and set theory. Content. Chapter 1 Set Theory 1.1 Basic definitions and notation A set is a collection of objects. Boolean algebra Fuzzy sets and systems Gödel's theorem Lattice (mathematics) Logic Postulate Recursive function Set theory Theorem. One of the most useful tools of logic and mathematics is set theory. 10.3 Basic Logical Operations. Examples of countable ordinals. 9.7 Paradoxes in Set Theory. 2. Back to Top Back to Top. Gain an appreciation of the usefulness and limitations of the development of theories from axioms. Cardinal arithmetic. Uncountable ordinals and Hartogs’ lemma. 10.4 Propositions and Truth Tables. They are not guaran-teed to be comprehensive of the material covered in the course. 10.6 Logical Equivalence.