hidden - assigned and confirmed by the Study Dept.
Date of registration:
26.05.2011
Date of assignment:
26.05.2011
Administrator's approval:
not processed yet
Date and time of defence:
19.09.2013 12:00
Date of electronic submission:
19.08.2013
Date of proceeded defence:
19.09.2013
Submitted/finalized:
committed by student and finalized
Opponents:
RNDr. David Chodounský, Ph.D.
Guidelines
Práce zkoumá logické základy forcingu. Práce ukáže, do jaké míry lze forcing formalizovat tak, aby nemusel předpokládat, že existuje tranzitivní model ZFC. Dokonce lze forcingovou kontrukci vyjádřit i v PA (práce zkoumá meze tohoto vyjádření). Součástí práce je uvedení a důkaz základních forcingových vět, včetně několika příkladů (Cohen, Sacks). Součástí práce je přehled interpretačních technik (interpretace jedné teorie v druhé) a jejich souvislost s forcingem.
References
Kenneth Kunen, Set theory: An introduction to Independence proofs, Elsevier. Tomas Jech, Set theory, Springer. Vítězslav Švejdar, Logika: Neúplnost, složitost, nutnost, Academia.
Preliminary scope of work
The work studies the logical foundations of the method of forcing. The work shall show how to interpret forcing so that it does not need to presume the existence of a countable transitive model of ZFC. The forcing contrustion can be expressed even in PA (the work shall study the constraints of this expressibility in PA). The work shall include a review of the basic forcing theorems, and also examples of some of the best-known forcing constructions (eg. Cohen and Sacks forcing). The work shall review the technique of interpreting one theory in another, and will study the connections with forcing.
Preliminary scope of work in English
The work studies the logical foundations of the method of forcing. The work shall show how to interpret forcing so that it does not need to presume the existence of a countable transitive model of ZFC. The forcing contrustion can be expressed even in PA (the work shall study the constraints of this expressibility in PA). The work shall include a review of the basic forcing theorems, and also examples of some of the best-known forcing constructions (eg. Cohen and Sacks forcing). The work shall review the technique of interpreting one theory in another, and will study the connections with forcing.