標(biāo)題: Titlebook: An Algebraic Introduction to Mathematical Logic; Donald W. Barnes,John M. Mack Textbook 1975 Springer Science+Business Media New York 1975 [打印本頁(yè)] 作者: Corticosteroids 時(shí)間: 2025-3-21 19:51
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作者: 乳白光 時(shí)間: 2025-3-21 23:08
https://doi.org/10.1007/978-3-642-47386-9instruction of the list is applicable, producing a result to which exactly one instruction is applicable, until after a finite (but not necessarily bounded) number of steps, the process stops and a decision is announced.作者: HPA533 時(shí)間: 2025-3-22 03:13
0072-5285 on on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same978-1-4757-4491-0978-1-4757-4489-7Series ISSN 0072-5285 Series E-ISSN 2197-5612 作者: 量被毀壞 時(shí)間: 2025-3-22 05:08 作者: synovial-joint 時(shí)間: 2025-3-22 12:21 作者: 憤怒歷史 時(shí)間: 2025-3-22 13:46
Propositional Calculus,odel of the system to be studied, and then conduct what is essentially a pure mathematical investigation of the properties of our model. Since this book is intended for mathematicians, the system we propose to study is not general logic but the logic used in mathematics. By this restriction, we achi作者: dowagers-hump 時(shí)間: 2025-3-22 20:44
Predicate Calculus,en collection of “primitive” statements is enlarged by combining statements. The Propositional Calculus does not analyse the original primitive statements. Our aim now is to construct a more complicated model of mathematical reasoning, which incorporates more of the ordinary features of this reasoni作者: 絕緣 時(shí)間: 2025-3-22 22:01
First-Order Mathematics,onstructed within the first-order predicate calculus will be called a first-order theory. By comparing a first-order theory with the informal theory on which it is modelled, we may gain insight into the influence of our logical system on our mathematics.作者: 一窩小鳥 時(shí)間: 2025-3-23 04:45 作者: 狗窩 時(shí)間: 2025-3-23 06:07 作者: fidelity 時(shí)間: 2025-3-23 11:59 作者: 壓倒 時(shí)間: 2025-3-23 14:08
,Turing Machines and G?del Numbers,d that no such procedure exists for Pred(., .). Before attempting to prove this non-existence theorem, we must say more precisely what we mean by “procedure”. The procedures we shall discuss are called decision processes, and informally we think of a decision process as a list of instructions which 作者: fringe 時(shí)間: 2025-3-23 18:51 作者: 熱情贊揚(yáng) 時(shí)間: 2025-3-23 23:44 作者: 懶惰民族 時(shí)間: 2025-3-24 02:24 作者: SLING 時(shí)間: 2025-3-24 09:27 作者: 生命 時(shí)間: 2025-3-24 11:04 作者: 觀點(diǎn) 時(shí)間: 2025-3-24 18:36
https://doi.org/10.1007/978-3-662-02181-1e system we wish to study. Such models have been constructed as ultrapowers in Chapter VII. In this chapter, we investigate ways of exploiting such models in the study of a standard system. We begin by considering elementary systems, i.e., systems in which relations between elements, but not properties of subsets, can be studied.作者: orthodox 時(shí)間: 2025-3-24 22:48 作者: Conflict 時(shí)間: 2025-3-25 00:43
Die Vererbungsgesetze und der Mensch, group theory. The pervasive role of set theory in mathematics implies that any reasonable model of set theory will in effect contain a model of all of mathematics (including the mathematics of this book).作者: 后來(lái) 時(shí)間: 2025-3-25 06:07 作者: 自戀 時(shí)間: 2025-3-25 10:33
Zermelo-Fraenkel Set Theory, group theory. The pervasive role of set theory in mathematics implies that any reasonable model of set theory will in effect contain a model of all of mathematics (including the mathematics of this book).作者: Reclaim 時(shí)間: 2025-3-25 13:52 作者: GRAZE 時(shí)間: 2025-3-25 16:10 作者: 廢墟 時(shí)間: 2025-3-25 20:31
Properties of the Propositional Calculus,The properties of the Propositional Calculus that are of interest are those that arise in studying the relation between truth and proof. These properties are important features in the study of any formal system of reasoning, and we begin with some general definitions.作者: Glaci冰 時(shí)間: 2025-3-26 00:39 作者: Spinal-Fusion 時(shí)間: 2025-3-26 07:22 作者: CON 時(shí)間: 2025-3-26 12:15 作者: conservative 時(shí)間: 2025-3-26 15:10
Graduate Texts in Mathematicshttp://image.papertrans.cn/a/image/154814.jpg作者: 樂器演奏者 時(shí)間: 2025-3-26 17:59
Die Lehre von der Einzelwirtschaftnsisting of sets with certain operations satisfying certain conditions. The reader will also be aware that ideas and theorems, useful for the study of one type of system, can frequently be adapted to other related systems by making the obvious necessary modifications.作者: ALT 時(shí)間: 2025-3-27 00:32
Erbliche und nichterbliche Eigenschaften,odel of the system to be studied, and then conduct what is essentially a pure mathematical investigation of the properties of our model. Since this book is intended for mathematicians, the system we propose to study is not general logic but the logic used in mathematics. By this restriction, we achi作者: GLEAN 時(shí)間: 2025-3-27 05:07 作者: 極端的正確性 時(shí)間: 2025-3-27 07:03
Die Entstehung neuer Erbeigenschaften,onstructed within the first-order predicate calculus will be called a first-order theory. By comparing a first-order theory with the informal theory on which it is modelled, we may gain insight into the influence of our logical system on our mathematics.作者: annexation 時(shí)間: 2025-3-27 09:50
Die Vererbungsgesetze und der Mensch,s must include some form of set theory, for otherwise our study must be restrictive. For example, Elementary Group Theory formalises almost nothing of group theory. The pervasive role of set theory in mathematics implies that any reasonable model of set theory will in effect contain a model of all o作者: AWL 時(shí)間: 2025-3-27 15:51 作者: 保存 時(shí)間: 2025-3-27 17:48
https://doi.org/10.1007/978-3-662-02181-1e complex numbers, each of which is regarded as a unique system. When we attempt to study one of these systems by axiomatising it within the first-order predicate calculus, we find that our axiomatisation cannot be categorical, and that there exist models of our axiomatic theory not isomorphic to th作者: ACTIN 時(shí)間: 2025-3-28 00:04
https://doi.org/10.1007/978-3-642-47386-9d that no such procedure exists for Pred(., .). Before attempting to prove this non-existence theorem, we must say more precisely what we mean by “procedure”. The procedures we shall discuss are called decision processes, and informally we think of a decision process as a list of instructions which 作者: 初次登臺(tái) 時(shí)間: 2025-3-28 02:09
E. Blanck,F. Giesecke,H. Stremme N.. Accordingly, in order to show that a particular function .:N. → N is recursive, we must construct a Turing machine which computes .. This is a tiresome process, even for functions of relatively simple form, and consequently it is natural to seek an alternative characterisation of recursive func作者: 易碎 時(shí)間: 2025-3-28 06:42 作者: 從容 時(shí)間: 2025-3-28 11:45 作者: BROW 時(shí)間: 2025-3-28 17:02
Die Entstehung neuer Erbeigenschaften,en collection of “primitive” statements is enlarged by combining statements. The Propositional Calculus does not analyse the original primitive statements. Our aim now is to construct a more complicated model of mathematical reasoning, which incorporates more of the ordinary features of this reasoning.作者: 長(zhǎng)矛 時(shí)間: 2025-3-28 22:38
Die Entstehung neuer Erbeigenschaften,onstructed within the first-order predicate calculus will be called a first-order theory. By comparing a first-order theory with the informal theory on which it is modelled, we may gain insight into the influence of our logical system on our mathematics.作者: 玩笑 時(shí)間: 2025-3-29 01:55
E. Blanck,F. Giesecke,H. Stremme N.. Accordingly, in order to show that a particular function .:N. → N is recursive, we must construct a Turing machine which computes .. This is a tiresome process, even for functions of relatively simple form, and consequently it is natural to seek an alternative characterisation of recursive functions that will facilitate their recognition.作者: Self-Help-Group 時(shí)間: 2025-3-29 03:22
Universal Algebra,nsisting of sets with certain operations satisfying certain conditions. The reader will also be aware that ideas and theorems, useful for the study of one type of system, can frequently be adapted to other related systems by making the obvious necessary modifications.作者: 背帶 時(shí)間: 2025-3-29 09:22
Predicate Calculus,en collection of “primitive” statements is enlarged by combining statements. The Propositional Calculus does not analyse the original primitive statements. Our aim now is to construct a more complicated model of mathematical reasoning, which incorporates more of the ordinary features of this reasoning.作者: 貿(mào)易 時(shí)間: 2025-3-29 13:06
