Foundations of Measurement: Representation, axiomatization, and invariance
Courier Corporation, 2007 - Mathematics - 356 pages
This classic series in the field of quantitative measurement established the formal foundations for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence. Volume III examines representation as expressed in axiomatization and invariance.
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1-point homogeneous 1-point unique additive conjoint algebraic Archimedean axiom Archimedean properties automor automorphism group axiomatizable axiomatization binary operation binary relation bisymmetric Chapter concept conjoint structure construction COROLLARY Dedekind complete deﬁnability deﬁned deﬁnition dimensionally invariant distribution domain elementary language elementary theory empirical relational endomorphism Equation equivalent example exists extensive measurement ﬁnitary class ﬁnite models ﬁrst ﬁrst-order ﬁxed point formulated function composition homomorphism idempotent identity iﬁ iﬂ induced inﬁnite integer isomorphic Lemma logic Luce mapping mathematical meaningful measurement structures minimal element monotonicity multiplication Narens nonadditive nonempty nonlogical numerical relation numerical representation order topology ordered group PCSs phisms physical positive proof properties prove ratio scales real numbers reference invariant relation symbol relational structure restricted result satisﬁes scale type Section solvable speciﬁc standard sequence structure invariant subgroup submodel subset Suppose Theorem Thomsen condition tion topology totally ordered universal sentence variables weak order