Countable or Uncountable*That is the question!
... • Similarly Q- can be thought of as a subset of NxN • Q+ υ {0} and Q- are countable because they are subsets of a countable set. • We have shown that the union of two countable sets is also countable so (Q+ υ {0}) υ Q- = Q is countable ...
... • Similarly Q- can be thought of as a subset of NxN • Q+ υ {0} and Q- are countable because they are subsets of a countable set. • We have shown that the union of two countable sets is also countable so (Q+ υ {0}) υ Q- = Q is countable ...
A Relationship Between the Fibonacci Sequence and Cantor`s
... The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural numbe ...
... The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural numbe ...
BEYOND FIRST ORDER LOGIC: FROM NUMBER OF
... non-elementary model theory. Non-elementary model theory studies formal languages other than ‘elementary’ or first order logic; most of them extend first order. We began by declaring that model theory studies classes of models. Traditionally, each class is the collection of models that satisfy some ...
... non-elementary model theory. Non-elementary model theory studies formal languages other than ‘elementary’ or first order logic; most of them extend first order. We began by declaring that model theory studies classes of models. Traditionally, each class is the collection of models that satisfy some ...
Beyond first order logic: From number of structures to structure of
... method would endorse ‘proof in metamathematics or set theory’ while the syntactic method seeks a ‘proof in some formal system’. Traditionally model theory is seen as the intersection of these two approaches. Chang and Keisler[17] write: universal algebra + logic = model theory. Juliette Kennedy[33] ...
... method would endorse ‘proof in metamathematics or set theory’ while the syntactic method seeks a ‘proof in some formal system’. Traditionally model theory is seen as the intersection of these two approaches. Chang and Keisler[17] write: universal algebra + logic = model theory. Juliette Kennedy[33] ...
ON PRESERVING 1. Introduction The
... which are inconsistent. For consider, if conX (Γ) and Y preserves the X consistency predicate then conX (CY (Γ)). Suppose that Γ is not Y -consistent, then CY (Γ) = S. By [R] CX (CY (Γ)) = CX (S) = S which is to say that CY (Γ) is not X-consistent, a contradiction. Similarly for the argument that Γ ...
... which are inconsistent. For consider, if conX (Γ) and Y preserves the X consistency predicate then conX (CY (Γ)). Suppose that Γ is not Y -consistent, then CY (Γ) = S. By [R] CX (CY (Γ)) = CX (S) = S which is to say that CY (Γ) is not X-consistent, a contradiction. Similarly for the argument that Γ ...
Annals of Pure and Applied Logic Ordinal machines and admissible
... within a discrete time axis which is also indexed by ω. In [5], the first author defined ordinal Turing machines by replacing the set ω of natural numbers by the class Ord of ordinal numbers. In this article we generalize both standard and ordinal Turing machines to α -Turing machines, or α -machine ...
... within a discrete time axis which is also indexed by ω. In [5], the first author defined ordinal Turing machines by replacing the set ω of natural numbers by the class Ord of ordinal numbers. In this article we generalize both standard and ordinal Turing machines to α -Turing machines, or α -machine ...
On the strength of the finite intersection principle
... P intersection principle (P IP). Every nontrivial family of sets has a maximal subfamily with the P intersection property. Following common usage, we shall refer to a given family as an instance of P IP, and to a maximal subfamily with the P intersection property as a solution to this instance. The ...
... P intersection principle (P IP). Every nontrivial family of sets has a maximal subfamily with the P intersection property. Following common usage, we shall refer to a given family as an instance of P IP, and to a maximal subfamily with the P intersection property as a solution to this instance. The ...
ON LOVELY PAIRS OF GEOMETRIC STRUCTURES 1. Introduction
... The previous result has the following consequence: Corollary 2.8. All lovely pairs of models of T are elementarily equivalent. We write TP for the common complete theory of all lovely pairs of models of T . To axiomatize TP we follow the ideas of [24, Prop 2.15]. Here we use for the first time that ...
... The previous result has the following consequence: Corollary 2.8. All lovely pairs of models of T are elementarily equivalent. We write TP for the common complete theory of all lovely pairs of models of T . To axiomatize TP we follow the ideas of [24, Prop 2.15]. Here we use for the first time that ...
The disjunction introduction rule: Syntactic and semantics
... Obviously, this fact could be interpreted as evidence that the mental models theory holds, since it appears to show that people only reason considering semantic models, and not formal or syntactic rules. However, this problem does not really affect theories such as the mental logic theory. As indica ...
... Obviously, this fact could be interpreted as evidence that the mental models theory holds, since it appears to show that people only reason considering semantic models, and not formal or syntactic rules. However, this problem does not really affect theories such as the mental logic theory. As indica ...
