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...dentify the α-th member of that class, i.e. one can index (count) them. A class is closed and unbounded if its indexing function is continuous and never st ...entical, and to seek a "canonical" representative of the isomorphism type (class). This is exactly what the ordinals provide, and it also provides a canoni

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...makes it convenient to lump signs and interpretants together into a single class called the ''syntactic domain''. In the forthcoming examples <math>S\!</ma ==Semiotic equivalence relations==

<div class="nonumtoc">__TOC__</div> ...s use, namely, the conditions of the definition that lead up to the stated equivalence. The relevant STR is recorded in Rule&nbsp;1. By way of convention, I lis

...'nodes'' or ''vertices'') and two mappings from the class of arrows to the class of objects, called ''source'' and ''target'' (often also ''domain'' and ''c ...n interesting categories from deductive systems by imposing an appropriate equivalence relation on proofs.</p>

The first order of business is to describe the general class of The logical class of cacti is the broadest, encompassing the whole species

...simply the models of the equational theory of two values, and observes the equivalence of both the lattice and ring definitions to this more elementary one.'' ...ties can be stated as, every class of models of the equational theory of a class ''C'' of algebras is the Homomorphic image of a Subalgebra of a direct Prod

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...ask ahead is to chart a course from general ideas about ''transformational equivalence classes of graphs'' to a notion of ''differential analytic turing automata' ...transformation rules partitions the set of graphs into ''transformational equivalence classes'' (TECs).

...Incidentally, though, it will also be convenient to take in the case of a class or collection of individuals with no pertinent inner structure as a trivial ...these may be treated as the canonical representatives of their respective equivalence classes.

...import, something that might be referred to as their ''logical equivalence class'' (LEC), and that we could as well call the ''constraint information'' or t ...o contemplate is how to characterize them as two species of a very general class.

...s eye view in question is more formally known as the perspective of formal equivalence, from which remove one cannot see many distinctions that appear momentous f ...induce its [[partition of a set|partition]] into exactly two [[equivalence class]]es, is what [[George Spencer Brown]] called the ''primary arithmetic''.

...omputational representation, the expressions of this calculus parse into a class of tree-like data structures called ''painted cacti''. This is a family of ...e former class of data structures, leaving the consideration of the latter class to a part of the project where their distinctive features are key to develo

<div class="nonumtoc">__TOC__</div> ...as denoting either (1) a class of entities or (2) all of the members of a class of entities, depending on which interpretation the reader prefers. These t

<div class="nonumtoc">__TOC__</div> ...nd (2) to focus on special cases of pragmatic transformations in which one class of entities is fixed.

<div class="nonumtoc">__TOC__</div> ...name{and}~ S^{\prime\prime\prime}\!</math> are taken at random from such a class that their characters at random are such as <math>{P^{\prime}, P^{\prime\pr

This section introduces the class of mathematical objects known as proposition fields. These are structures w ...purely superficial change, since the analytic expansion preserves logical equivalence with the original proposition, but the good of a particular form for a part

...attributes and so connote them as to determine what they denote. To this class belong all ''words'' and all ''conceptions''. Most combinations of words a ...r. Since they have no common character which does not belong to the whole class of mammals, it is plain that ''mammals'' may be substituted for this term.

Let !X! = {x_1, ..., x_k} be a finite class of variables -- is commonly known as "logical equivalence",

<div class="nonumtoc">__TOC__</div> ...digm.''' Generic example that reflects significant properties of a target class of phenomena, often derived from a tradition of study.

<p>The second class embraces terms whose logical form involves the conception of relation, and <p>The third class embraces terms whose logical form involves the conception of bringing thing

nominally or reconstructed rationally as equivalence classes of signs. their semantic equivalence classes. This transformation of a relation

| Again, if the letter 'M' stands for a differentiable manifold (of class C^oo) | B is called a 'natural equivalence' or better a 'natural isomorphism';

...and the positive, may be viewed as two different ways of generalizing the class of basic propositions. ...proposition of the form <math>(X \land Y) \Rightarrow Z.</math> But this equivalence should remind us of the functional isomorphism that exists between a constr

...is tantamount to the logical function that is commonly known as ''logical equivalence'', or just plain ''equality'':</p> ...a considerable generalization of these regular representations to a broad class of relational algebraic systems in Peirce's earliest papers. The crux of t

<p>This double way of regarding a class-term as a whole of parts is remarked by Aristotle in several places (e.g., <p>There is a large class of reasonings which are neither deductive nor inductive. I mean the infere

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...r or the positive, may be viewed as two different ways of generalizing the class of simple projections. The linear and the positive propositions are genera ...f the form (''X''&nbsp;&and;&nbsp;''Y'')&nbsp;&rArr;&nbsp;''Z''. But this equivalence should remind us of the functional isomorphism that exists between a constr

<div class="nonumtoc">__TOC__</div> a target class of phenomena, often derived from a tradition of study.

<div class="nonumtoc">__TOC__</div> ...hin the practical constraints of a computational medium and preserving the equivalence of information. To illustrate the kinds of technical issues that are invol

...elf prove that it is unworkable, but it does place the idea in a different class. ...y driven system is intended to capture the essential properties of a broad class of intelligent systems, and to highlight the crucial processes which suppor

...and the positive, may be viewed as two different ways of generalizing the class of basic propositions. ...proposition of the form <math>(X \land Y) \Rightarrow Z.</math> But this equivalence should remind us of the functional isomorphism that exists between a constr

...and the positive, may be viewed as two different ways of generalizing the class of basic propositions. ...proposition of the form <math>(X \land Y) \Rightarrow Z.</math> But this equivalence should remind us of the functional isomorphism that exists between a constr

...ting signs, into the membership relation that signs bear to their semantic equivalence classes. This transformation of a relation between signs and the world int ...definition of individual sign relations on analogy with another important class of three-place relations of broad significance in mathematics and far-reach

a broad class of relational algebraic systems in Peirce's earliest papers. the paper "On a Class of Multiple Algebras" (CP 3.324-327).

| proposition at bottom. In like manner a "term", or class-name, is | useless. But it will be more simple to class it among true