Brief Disclaimer
For those who haven’t read Mathematical Descriptions of Models A and G, I suggest you do so, as this article serves as an extension of this.
The Structure
Model V (created by Vladmir Vincent) is very much similar to Model A in the regard that for both models, acts on the set of 8 functions transitively, and both models would be classified under using GAP’s classification code of finite transitive groups and share the same automorphism class, but the key thing that separates them is that the elements used are different. In Model A, the standard information elements are used, whereas in Model V, elements that are shared by mirror pairs are used, which I will call ‘mirror elements’ (MEs for short). So, Model V can be described by (the set of functions) and the set
of mirror elements, or ‘information blocks’. Formally, acts via pre-compositions on the set of bijections from to in Model V and the set of types can be defined as all arrangements which result from applying every permutation in .
The Surjection
If we consider that and , then it can be extrapolated that the relationship between is surjective (one-to-many).
List of Surjections in Model A
Function 1: Identity, Kindred
Function 2: Mirror, Supervisee
Function 3: Superego, Lookalike
Function 4: Conflictor, Supervisor
Function 5: Dual, Semi-dual
Function 6: Activator, Beneficiary
Function 7: Extinguisher, Mirage
Function 8: Quasi-identical, Benefactor
List of Surjections in Model V
Function 1: Identity, Mirror
Function 2: Kindred, Supervisor
Function 3: Superego, Conflictor
Function 4: Lookalike, Supervisee
Function 5: Dual, Activator
Function 6: Semi-dual, Benefactor
Function 7: Extinguisher, Quasi-identical
Function 8: Mirage, Beneficiary
It is interesting of note that for both sets of functions that the elements that are shared between the models are all contained in the Process/Result subgroup, in the sense that for example that there is only one for a Process type.
Systems of Injections for Model V
An acceptable system of injections on Model V must arise from an index-2 subgroup of corresponding to a converse dichotomy. These include Irrational/Rational, Extroverted/Introverted, Process/Result, and Questim/Declatim.
The reason for this restriction is structural. Each mirror element admits a decomposition into its associated monadic elements in , and any admissible injection must preserve this correspondence. Equivalently, for every function in either the unsplit element or exactly one of its associated monadic refinements must be present, uniformly across all types.
Index-2 subgroups not associated with converse dichotomies (these are the vector dichotomies, which when intersected define the ‘Challenge Response’ tetrachotomy) fail to satisfy this condition, as they induce splittings that cannot be reconciled with the monadic decomposition of elements in . Consequently, no other index-2 subgroup of satisfies the uniform monadic-refinement constraint above.
Classification Proposal of the ‘V-Models’
: Model defined by the full transitive action on the set of 8 functions. Baseline Model V with the Mirror Elements (MEs).
: Model that is theoretical. Irrational/Rational serves as the basis here, which has a transitive action on the set of 8 functions.
: Theoretical model. The basis is Extroverted/Introverted which acts transitively on the set of 8 functions.
: Model deployed by the School of Classical Socionics (SCS) and School of Humanitarian Socionics (SHS) for Model G. The basis is Process/Result which acts transitively on the set of 8 functions.
: Model that is theoretical. Positivist/Negativist is the basis here, which acts transitively on the set of 8 functions.