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  • Set theory is both the framework for all mathematics and a mathematical discipline in its own right. The main focus of the project connects both these parts as it studies one of the basic concepts of set theory, i.e. how many there are subsets of a given set depending on the richness of the structure of the universe of sets. More specifically, I will analyze the effects of existence of certain large cardinals on the function which assigns to each regular cardinal number the number of the subsets of the cardinal (so called Easton function). Further, I will study the behaviour of cardinal numbers and of cardinal arithmetics with the scope extended to include singular cardinal numbers as well. A part of the results was already published in a prestigious international journal Annals of Pure and Applied Logic [1]. On a broader scale, the project will study the possibility of extending the purely set-theoretical framework of the project  to include other parts of mathematics, for instance recursion theory or proof theory. Last but not least, in cooperation with the KGRC research centre in Vienna and Mathematical institute AV CR, I plan to give a series of regular lectures on advanced set-theoretical topics to raise awareness of the set theory among general mathematical audience. [1] Sy D. Friedman and Radek Honzik, Easton Function and Large Cardinals, Annals of Pure and Applied Logic (2008), doi:10.1016/j.apal.2008.02.001 (v tisku). (en)
  • Cílem projektu je identifikovat seznam podmínek spolu s jejich logickou optimalitou, které charakterizují chování funkce kontinua vzhledem k velkým kardinálům. Dalším cílem je rozšíření množinově-teoretických postupů do dalších oblastí matematiky a logiky, tj. dosažení interdisciplinárního přesahu.
Title
  • Logical and set-theoretical properties of the continuum function (en)
  • Logické a množinově-teoretické vlastnosti funkce kontinua
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  • GP201/09/P115
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  • množina; potence množiny; Eastonova funkce; forcing; velký kardinál; konsistence (en)
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  • The project was excellent, both in terms of expertise and in terms of disbursement of funds. (en)
  • Řešení projektu proběhlo na vynikající úrovni, a to jak z hlediska odborného tak i z hlediska čerpání finančních prostředků. (cs)
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  • Eastonova funkce
  • forcing
  • potence množiny
  • velký kardinál
  • množina
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