Challenges of traditional logic was to present wascator a systematic wascator way to determine the

For Gödel sentence (the word may prove sentences such as) is not a general statement mathematicians are interested. However, the sentence can not prove gatjiman interest. For example, the continuum hypothesis (Continuum hypothesis). Apart. wascator Continuum hypothesis, wascator according to Gödel and Cohen (P. J Cohen) is not determined by the ZFC. (Undecidable) Cohen that the hypothesis is that Gödel was inconsistent wascator proved to be true that the inconsistent that each of these hypotheses are false .
2. There is a world of sets that are intended by ZF. That of course did not strictly presented. (Based on the size, Power set problem of an infinite set of sets), we are not able to understand the circumstances set can not be written (for example, so the Power set of natural numbers. Natural a set of power - is a natural number and a 1: 1 is non-uncoutable) also repeated an infinite wascator system is assumed that this concept (Eterative conception) is also nebulous a concept (realism can not be described by the set of natural numbers if it's the same power law. It is not a reality but insisted it was not, constructivists will be rejected.)
Completeness: Γ φ If Γ φ / φ a payoff statement from the set Γ, φ is a derivation of the sentence set Γ.
Starting with an infinite number of sentences, but it boils down to what this means, finite sentence beginning, not the consequence is that no sentence. Compactness wascator theorem, there must be such a model is not intended in the natural model of the infinite, wascator if established.
Can be expressed in a sentence of the language we are having Countable. LS is shown that the model of this language is not always categorical. Consider wascator a system of technical mistakes, mistakes more than the natural numbers. LS means that this model is Countable one satisfying wascator the system with respect to a system having a Countable vocabulary. Countable and that one model is not a mistake for Model that we intended. (This comes from LS according to the simplest version.)
* Downward wascator Lőwenheim-Skolem theorem: let Γ be a set of sentences in a language of cardinality k, and let k <λ. wascator If Γ has a model of carinality λ, then Γ has a model of cardinality k ', with k k' <λ (k size of the sentence set for Γ if Γ has a larger than the size of the model λ k, the Γ There are k k '<λ of k' the size of the model to meet.)
This shows that the FOL has a limit on the power of expression. In other words, there is a limit to our communication. Even if you both understand and say that indeed there may be a different world. But this is different story goes beyond a secondary wascator logical. Secondary and secondary quantifier logic includes the X, X. Peano axioms are presented in SOL SOL is stronger because the expression will exclude wascator the non-standard model (non-standard model, unintended models).
But instead of SOL allows strong expression, the SOL Completeness is not true. In other words, it is not possible to draw all the consequences sentence in the SOL. (However, if the SOL will deal only with the halgeot have to deal with well defined model Full model does not differ significantly from the FOL.) This can be seen from the first theorem of Gödel . In that sense, it is impossible to present the SOL to the type system.
Challenges of traditional logic was to present wascator a systematic wascator way to determine the arguments that are not relevant and valid (Valid) demonstration. But if it implies that there is a mechanical process that is not fair and reasonable arguments covering demonstrations, such planning is impossible. A. The impossibility of this decision (Undeciability) of the FOL's Church. (FOL impossibility of decision, there is no mechanical procedure for calculating the yield of T and F in the argument is not valid in a reasonable argument for any argument in FOL This is closely related to arrangement of Gödel.)
The conditions that must be satisfied with this logic, at least something is a problem. Jyeotdeut decision possibility could not be shown on the conditions. Quine argued that perfection can be a condition. That is why Quine rejects the SOL SOL is incomplete wascator in that. (Quine is ridiculed SOL wrote that come in sheep, that is, in fact, seems like a logical system is to see that the set theory. wascator SOL is to the ontological wascator commitment see that.)
2. The claim is that the mathematical concept of Frege can be defined as a logical concept. (For the ZF is defined as the Membership relation, however, is that even Frege is defined as a logical concept.) If accepted by this ontological (ontological can be considered a logical attention) as defined in the claims to ontological reduction. For example, wascator to argue that it is a combination of atoms desk means to reduce the desk to the original growing presence. Frege as the target concept, ZF is that a reduction in the number of a set of ontological. However, the claim that it can not be reduced Benacerraf. Benacerraf, and that all the way to define a second very diverse, wascator important claims that position in the sequence or structure. This is the structure-liberal stance.
Good evening. Ye came while searching, I read well. One years ago, one of Cohen's forcing you to wonder how it differs from the configuration possibilities and techniques that Gödel found here and there. Let's read I was just kind of set theory obtained kunend, I'm poorly. Read this book its own basic modern algebra that preparing for, set theory, logic book I (general education is not an instructional books) the hangwonssik have read, too. I can not read well ttwini across some of the first to see signs. If you have text that explains the difference between the quantum jusipsa easily lump May I introduce you ask? It is not too hard 2010/11/09 20:37 #
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