Namespaces
Variants
Actions

Difference between revisions of "Domain of individuals (in logic)"

From Encyclopedia of Mathematics
Jump to: navigation, search
(TeX)
(Category:Logic and foundations)
Line 2: Line 2:
 
''universe''
 
''universe''
  
A term in [[Model theory|model theory]] denoting the domain of variation of individual (object) variables of a given formal language of first-order predicate calculus. Each such language is completely described by the set
+
A term in [[model theory]] denoting the domain of variation of individual (object) variables of a given formal language of first-order predicate calculus. Each such language is completely described by the set
  
 
$$L=\{P_0,\ldots,P_n,\ldots,F_0,\ldots,F_m,\ldots\}$$
 
$$L=\{P_0,\ldots,P_n,\ldots,F_0,\ldots,F_m,\ldots\}$$
Line 9: Line 9:
  
 
====References====
 
====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  S.C. Kleene,  "Mathematical logic" , Wiley  (1967)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  C.C. Chang,  H.J. Keisler,  "Model theory" , North-Holland  (1973)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  Yu.L. Ershov,  E.A. Palyutin,  "Mathematical logic" , Moscow  (1987)  (In Russian)</TD></TR></table>
+
<table>
 +
<TR><TD valign="top">[1]</TD> <TD valign="top">  S.C. Kleene,  "Mathematical logic" , Wiley  (1967)</TD></TR>
 +
<TR><TD valign="top">[2]</TD> <TD valign="top">  C.C. Chang,  H.J. Keisler,  "Model theory" , North-Holland  (1973)</TD></TR>
 +
<TR><TD valign="top">[3]</TD> <TD valign="top">  Yu.L. Ershov,  E.A. Palyutin,  "Mathematical logic" , Moscow  (1987)  (In Russian)</TD></TR>
 +
</table>
 +
 
 +
[[Category:Logic and foundations]]

Revision as of 21:48, 17 October 2014

universe

A term in model theory denoting the domain of variation of individual (object) variables of a given formal language of first-order predicate calculus. Each such language is completely described by the set

$$L=\{P_0,\ldots,P_n,\ldots,F_0,\ldots,F_m,\ldots\}$$

where $P_0,\ldots,P_n,\ldots,$ are predicate symbols and $F_0,\ldots,F_m,\ldots,$ are function symbols for each of which a number of argument places is given. A model $\mathfrak M$ (or an algebraic system) of $L$ is given by a non-empty set $M$ and an interpreting function $I$, defined on $L$ and assigning an $n$-place predicate to an $n$-place predicate symbol, i.e. a subset of the Cartesian power $M^n$ of $M$, and an $n$-place function $M^n\to M$ to an $n$-place function symbol. The set $M$ is called the domain of individuals (or universe) of the model $\mathfrak M$.

References

[1] S.C. Kleene, "Mathematical logic" , Wiley (1967)
[2] C.C. Chang, H.J. Keisler, "Model theory" , North-Holland (1973)
[3] Yu.L. Ershov, E.A. Palyutin, "Mathematical logic" , Moscow (1987) (In Russian)
How to Cite This Entry:
Domain of individuals (in logic). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Domain_of_individuals_(in_logic)&oldid=33766
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article