| Herbert B.Enderton哈佛大学博士，师从著名哲学家Hilary Putnam。曾任教于加州大学伯克利分校。现为加州大学洛杉矶分校数学系兼职教授，该校“逻辑学论坛”主席。曾担任《符号逻辑学会评论》杂志的主编。除本书外，他还著有另外两本广受好评的教材A Mathematical Introduction to Logic（本书影印版《数理逻辑》已由本社出版。）和Linear Algebra。... .. << 查看详细 |
| chapter 1 introduction . baby set theory 1 sets--an informal view classes 10 axiomatic method 10 notation 13 historical notes 14 chapter 2 axioms and operations axioms 17 arbitrary unions and intersections 23 algebra of sets 27 epilogue 33 review exercises 33 chapter 3 relations and functions ordered pairs 35 relations 39 n-ary relations 41 functions 42 infinite cartesian products 54 equivalence relations 55 .ordering relations 62 review exercises 64 chapter 4 natural numbers inductive sets 67 peano's postulates 70 recursion on w 73 arithmetic 79 ordering on w 83 review exercises 88 chapter 5 construction of the real numbers .. integers 90 rational numbers 101 real numbers 111 summaries 121 two 123 chapter 6 cardinal numbers and the axiom of choice equinumerosity 128 finite sets 133 cardinal arithmetic 138 ordering cardinal numbers 145 axiom of choice 151 countable sets 159 arithmetic of infinite cardinals 162 continuum hypothesis 165 chapter 7 orderings and ordinals partial orderings 167 well orderings 172 replacement axioms 179 epsilon-lmages 182 lsomorphisms 184 ordinal numbers 187 debts paid 195 rank 200 chapter 8 ordinals and order types transfinite recursion again 209 alephs 212 ordinal operations 215 isomorphism types 220 arithmetic of order types 222 ordinal arithmetic 227 chapter 9 special topics well-founded relations 241 natural models 249 cofinality 257 appendix notation, logic, and proofs selected references for further study list of axioms index ... |
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