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By Günther Ludwig

Written within the culture of G. Ludwig’s groundbreaking works, this publication goals to elucidate and formulate extra exactly the primary principles of actual theories. via introducing a uncomplicated descriptive language of straightforward shape, during which it's attainable to formulate recorded proof, ambiguities of actual theories are shunned up to attainable. during this method the sector of physics that are supposed to be defined through a concept is dependent upon simple suggestions purely, i.e. techniques that may be defined and not using a idea. during this context the authors introduce a brand new notion of idealization and evaluation the method of learning new suggestions. they suspect that, whilst the theories are formulated inside an axiomatic foundation, ideas are available to many tough difficulties equivalent to the translation of actual theories, the kin among theories in addition to the advent of actual ideas. The publication addresses either physicists and philosophers of technological know-how and may inspire the reader to give a contribution to the certainty of the lasting middle of actual wisdom in regards to the genuine buildings of the realm.

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Sp of any echelons G1 , . . , Gp , then one can give oneself an element s = (s1 , . . , sp ) of the set G1 × · · · × Gp , which is also an echelon. If there is a relation R(x1 , . . , xp ), one can consider the relation R(x1 , . . , xp ) and x1 ∈ G1 and . . and xp ∈ Gp . Otherwise, one can also take R as a relation of only one x of G = G1 ×. ×Gp . , R(x) determines in G a subset H ⊂ G such that {x ∈ H ⊂ R(x) and x ∈ G}. 4 Set Theory 31 This set H was previously denoted by Ex (R(x) and x ∈ G).

En ) onto S(E1 , . . , En ) thus obtained is denoted by f1 , . . , fn S . If all fi are injective (respectively surjective), then f1 , . . , fn S is also injective (respectively surjective), which one can easily show because this is valid for each step P or × of the echelon construction scheme S. If fi are mappings of Ei onto Ei and gi of Ei onto Ei , one denotes the mapping of Ei onto Ei by gi fi . One has then g1 f1 , . . , gn fn S = g1 , . . , gn S f1 , . . , fn S . , injective and surjective), with gi = fi−1 , then f1 , .

2); and if M T is contradictory, then A is a theorem in M T . (c) If A is a theorem in M T , then “A or B” is a theorem in M T . (d) If B is a theorem in M T , then “A or B” is a theorem in M T . , “not A” as well as “not B” cannot be theorems in M T . The two criteria (a) and (b) fix the sense of “not,” and what we briefly indicate in the new form by bivalent logic. 4). 4) mentioned above (in particular to prove the deductions (a) to (e)). This is not necessary because the deductions obtained are for the most part “intuitively” obvious, and the reader is certainly accustomed to applying such logic and the methods of proof in mathematics.

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