000			02427nam a22002895i 4500
001			65426
005			20210505155847.0
010			_a978-1-4614-8854-5 _dcompra
090			_a65426
100			_a20150401d2014 k||y0pory50 ba
101			_aeng
102			_aUS
200			_aSet theory _bDocumento electrónico _ewith an introduction to real point sets _fAbhijit Dasgupta
210			_aNew York, NY _cSpringer _cBirkhäuser _d2014
215			_aXV, 444 p. _cil.
300			_aColocação: Online
303			_aWhat is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
606			_94432 _aTeoria dos conjuntos
606			_952909 _aTeoria dos pontos críticos
680			_aQA248
700			_958117 _aDasgupta _bAbhijit
801			_aPT _gRPC
856			_uhttp://dx.doi.org/10.1007/978-1-4614-8854-5
942			_2lcc _cF _n0