Review of the Constitution of the United Persons

Partitioned, part of partitioned

2008-11-09T08:27:00.000-08:00

[A is] partitioned <==> common knowledge partition [of A][C.f. the knowledge axiom: common knowledge ϕ ==> ϕ, i.e., if ϕ is common knowledge, then ϕ holds at all knowledge points (I, r, t) for points (r, t) of R.]part of partitioned [A] <==> one of the elements of the common knowledge partition [of A][c.f.]whereA : a set or a topological space

Set

2008-11-02T10:15:00.000-08:00

set <==> [c.f.]subset <==> [c.f.]

Potentially

2008-10-28T01:25:00.000-07:00

potentially <==> not common knowledge that not[Cf. the definition of possible]

Contradictory

2008-10-28T01:09:00.000-07:00

contradictory <==> [c.f.][Cf. the definition of possible]

State

2008-10-19T06:49:00.000-07:00

state [of A] <==> a part of a partitioned [A]whereA : a set or a topological space

Theorem of State Fairness

2008-10-19T00:07:00.000-07:00

The Theorem of State Fairness:Fair society can be that and only that society which is a state.Proof:Fair society can be that and only that society which is a state.I.e.,possibly fair society <==> society which is a stateWe should get from the left side of the biconditional connective to the right side, through biconditional connectives [c.f. the definition of theorem].possibly fair society <==>

Society

2008-10-18T03:08:00.000-07:00

y is a society <==> there is x such that x is a member of y

Open set, separation, connectedness, component

2008-10-17T04:01:00.000-07:00

Let A be a topological space with topology T.open set <==> "a subset U of A is an open set of A if U belongs to the collection T" [Munkres, Topology, 76.p.]separation of A <==> "a pair of U, V of disjoint nonempty open subsets of A whose union is A" [Munkres, Topology, 148.p.]A is connected <==> "if there does not exist a separation of A" [Munkres, Topology, 148.p.]components of A <==> connected

Partition, part of partition

2008-10-15T22:10:00.000-07:00

"A partition of a set A is a collection of disjoint nonempty subsets of A whose union is all of A." Munkres, Topology, 23.p.We extend the definition of partition [breaking up into pieces] above to include components of the topological space A.partition(i) of a set A(ii) of a topological space A<==>a collection [D] of(i) disjoint nonempty subsets of A whose union is A, or(ii) components of Apart

Topology, topological space

2008-10-15T20:43:00.000-07:00

"A topology on a set A is a collection T of subsets of A having the following properties(1) the empty set (0) and A are in T,(2) the union of the elements of any subcollection of T is in T, and(3) the intersection of the elements of any finite subcollection of T is in T.""A topological space is an ordered pair (A, T) consisting of a set A and a topology T on A, but we often omit specific mention

Possibly fair society: a supposed sufficient condition

2008-10-13T03:25:00.000-07:00

We suppose that the possibility to meet this necessary condition [i.e. that all members of the society are equal members of it] is (necessary and) sufficient for the possibility of fairness of societies.In order to show the possibility of the fairness of a society it is sufficient to show that this condition is not impossibile to meet (e.g. by showing that it is met).

Common knowledge

2008-10-06T00:23:00.000-07:00

common knowledge <==> CA under view-based knowledge interpretations, c.f. Halpern-Moses, "Knowledge and Common Knowledge in a Distributed Environment" [pdf],whereA : a set or a topological space of agentsThe properties of knowledge and common knowledge under view-based knowledge interpretations:"[...]the definition of knowledge in view-based interpretations agrees with the well-known modal logic

One

2008-10-05T23:52:00.000-07:00

one [<==> unique] <==> [c.f.]

Explicit

2008-10-05T23:40:00.000-07:00

explicit <==> [Coar, "The Open Source Definition"]

Element

2008-10-05T22:45:00.000-07:00

x is an element of y <==> [c.f.]

Implication

2008-10-05T12:48:00.000-07:00

implication <==> [c.f.]

As

2008-10-05T03:33:00.000-07:00

x as y <==> x is an element of y

Theorem

2008-10-05T03:24:00.000-07:00

C.f. Megill, Deductions vs. Theorems

(Social) equality

2008-10-05T03:19:00.000-07:00

(x = y) as z <==> there is z such that x and y are equal members of z <==> there is z such that x and y are equivalent in z[C.f., c.f., c.f., c.f. and c.f..]

Equivalent in

2008-10-05T03:15:00.000-07:00

x and y are equivalent in z <==> x is in z, and y is in z, and x and y are equivalent

Member

2008-10-05T02:59:00.000-07:00

x is a member of y <==> declared by x and y that x is an element of y

Equivalent as

2008-10-05T02:16:00.000-07:00

x and y are equivalent as z <==> x as z, and y as z, and x and y are equivalent

In

2008-10-05T02:02:00.000-07:00

x in y <==> x is a member of y

Definition

2008-10-04T07:57:00.001-07:00

definition <==> biconditional connective[C.f.][C.f.]

Distictly constituted, dictinctly constitute

2008-10-04T04:35:00.000-07:00

distinctly constituted <==> constituted based on and in order to the constitution consistentlydistinctly constitute <==> make distinctly constituted <==> make constituted based on and in order to the constitution consistently