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49 bytes removed ,  20:08, 28 July 2009
→‎Axioms: del unnec specs
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The axioms are just four in number, divided into the ''arithmetic initials'', <math>I_1\!</math> and <math>I_2,\!</math> and the ''algebraic initials'', <math>J_1\!</math> and <math>J_2.\!</math>
 
The axioms are just four in number, divided into the ''arithmetic initials'', <math>I_1\!</math> and <math>I_2,\!</math> and the ''algebraic initials'', <math>J_1\!</math> and <math>J_2.\!</math>
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{| align="center" border="0" cellpadding="10" cellspacing="0"
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{| align="center" cellpadding="10"
 
| [[Image:Logical_Graph_Figure_20.jpg|500px]] || (20)
 
| [[Image:Logical_Graph_Figure_20.jpg|500px]] || (20)
 
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One way of assigning logical meaning to the initial equations is known as the ''entitative interpretation'' (EN).  Under EN, the axioms read as follows:
 
One way of assigning logical meaning to the initial equations is known as the ''entitative interpretation'' (EN).  Under EN, the axioms read as follows:
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{| align="center" border="0" cellpadding="10"
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{| align="center" cellpadding="10"
 
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<math>\begin{array}{ccccc}
 
<math>\begin{array}{ccccc}
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Another way of assigning logical meaning to the initial equations is known as the ''existential interpretation'' (EX).  Under EX, the axioms read as follows:
 
Another way of assigning logical meaning to the initial equations is known as the ''existential interpretation'' (EX).  Under EX, the axioms read as follows:
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{| align="center" border="0" cellpadding="10"
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{| align="center" cellpadding="10"
 
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<math>\begin{array}{ccccc}
 
<math>\begin{array}{ccccc}
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